Question
Download Solution PDFएक नियमित बहुभुज के लिए, आंतरिक कोणों का योग, उसके बाह्य कोणों के योग से 200% अधिक है। बहुभुज के प्रत्येक आंतरिक कोण की माप x° है। x° का मान कितना है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
बहुभुज के सभी आंतरिक कोणों का योग बाह्य कोणों के योग से 200% अधिक है।
प्रयुक्त सूत्र:
एक बहुभुज के सभी आंतरिक कोणों का योग = (n - 2) × 180°
जहाँ n = भुजाओं की संख्या
गणना:
प्रश्नानुसार,
बहुभुज के आंतरिक कोणों का योग
= 360° का 300%
= 3 × 360°
= 1080°
एक बहुभुज के सभी आंतरिक कोणों का योग = (n - 2) × 180°
⇒ 1080° = (n - 2) × 180°
⇒ (1080°/180°) = (n- 2)
⇒ 6 = n - 2
⇒ n = 8
अब, प्रत्येक आंतरिक कोण x = 1080°/8 = 135°
∴ x का अभीष्ट मान 135° है।
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